Boyce E. Griffith

Boyce Griffith Boyce E. Griffith
Assistant Professor, Leon H. Charney Division of Cardiology, Department of Medicine
Affiliated Faculty, Computational Biology Program, Sackler Institute of Graduate Biomedical Sciences
Affiliated Faculty, NYU Center for Health Informatics and Bioinformatics
NYU School of Medicine
New York University
boyce.griffith@nyumc.org
griffith@cims.nyu.edu

Software

IBAMR: IBAMR is a distributed-memory parallel implementation of the immersed boundary (IB) method with support for Cartesian grid adaptive mesh refinement (AMR). Support for distributed-memory parallelism is via MPI, the Message Passing Interface. Support for spatial adaptivity is via SAMRAI, the Structured Adaptive Mesh Refinement Application Infrastructure, which is developed at the Center for Applied Scientific Computing at Lawrence Livermore National Laboratory.

This implementation of the IB method also makes extensive use of functionality provided by several high-quality third-party software libraries, including:

PETSc, the Portable, Extensible Toolkit for Scientific Computation,
hypre, a library of high performance preconditioners that features parallel multigrid methods for both structured and unstructured grid problems,
HDF5, a general purpose library and file format for storing scientific data,
Blitz++, a high-performance C++ array class library, and
Silo, a general purpose I/O library and file format for storing scientific data for visualization and post-processing.

IBAMR outputs visualization files that can be read by the VisIt Visualization Tool. Work is also underway to implement support for finite element mechanics models in IBAMR via the libMesh finite element library.

IBAMR source code is hosted by Google Code at http://ibamr.googlecode.com.

Multi-beat simulations of the fluid dynamics of the aortic heart valve with physiological driving and loading conditions using the immersed boundary method.

A model aortic valve is mounted in a semi-rigid aortic root model with anatomically realistic aortic sinuses. This "valve tester" is immersed in a fluid box. Pressure boundary conditions are imposed at the inlet (bottom) of the vessel using a prescribed left ventricular pressure waveform, and at the outlet (top) of the vessel using a Windkessel model. (See schematic diagram below.)

Schematic diagram showing how boundary conditions are imposed on the model vessel. At the upstream boundary, a time-dependent left-ventricular pressure waveform is prescribed. At the downstream boundary, the three-dimensional fluid-structure interaction model is coupled to a three-element Windkessel model fit to human data. Notice that the flow rate is not prescribed in this model, but rather emerges during the computation.

side view of the model aortic valve and vessel

top and side views of the model aortic valve

The opening and closing dynamics of the model aortic valve. The lower inset shows the prescribed driving pressure (blue curve) and computed loading pressure (green curve). The upper inset shows the computed flow rate through the model valve (blue curve). Net flow through the model valve is approximately 65 ml per cardiac cycle, which is within the physiological range. Notice that the flow rate is not specified in the model; rather, it emerges during the course of the fluid-structure interaction simulation. (Click on the above images to view linked Quicktime movies.)

side view of the model aortic valve and the axial (streamwise) fluid velocity

The opening and closing dynamics of the model aortic valve along with the axial (streamwise) fluid velocity. The fluid velocity is shown on a plane that bisects the model vessel and one of the model valve leaflets. Forward flow is indicated in red, reverse flow is indicated in blue. Notice that, except for the first beat, the model valve permits essentially no regurgitation during closure. (Click on the above image to view linked Quicktime movie.)

For further details, see: B.E. Griffith. Immersed boundary model of aortic heart valve dynamics with physiological driving and loading conditions. Int J Numer Meth Biomed Eng. 28: 317-345 (2012). (DOI, PDF)

Simulations of a prosthetic mitral heart valve using the immersed boundary method.

immersed boundary model of prosthetic mitral valve

A chorded prosthetic mitral valve (left panel) and the corresponding immersed boundary model (right panel).

The model mitral valve is mounted in a rigid tube that is immersed in a fluid box. Time-dependent velocity boundary conditions are prescribed at the upstream boundary (located at the left of the figure) and zero-pressure boundary conditions are prescribed at the downstream boundary (located at the right of the figure).

The opening and closing dynamics of the model prosthetic mitral valve viewed from the side (left panel) and top (right panel). (Click on the above images to view linked Quicktime movies.)

Streamlines during the opening phase of the model mitral valve.

For further details, see: B.E. Griffith, X. Luo, D.M. McQueen, and C.S. Peskin. Simulating the fluid dynamics of natural and prosthetic heart valves using the immersed boundary method. Int J Appl Mech. 1: 137-177 (2009). (DOI, PDF)

Simulations of the electrical function of the heart by an immersed boundary approach to the bidomain equations.

transmembrane potential difference and extracellular potential

transmembrane potential difference on a two-dimensional slice

transmembrane potential difference and extracellular potential on a two-dimensional slice

Click on the above images to view the corresponding animated GIFs.

Simulations of cardiac fluid mechanics by an adaptive version of the immersed boundary method.

Click on the above images to view the corresponding animated GIFs. Additional animations are available here, and an overview of the three-dimensional fiber structure of the heart and great vessels used in this work is available here.

Publications, talks, and other conference contributions
Curriculum Vitae (PDF)
Research Interests
Mathematical, numerical, and computational methods in medicine and biology; mathematical physiology, especially cardiac fluid-structure interaction, cardiac electrophysiology, and cardiac electro-mechanical interaction; adaptive numerical methods; parallel scientific computing.

Publications

L.J. Gray and B.E. Griffith. A faster Galerkin boundary integral algorithm. Comm Numer Meth Eng. 14: 1109-1117 (1998). (DOI, PDF)

S.J. Cox and B.E. Griffith. Recovering quasi-active properties of dendritic neurons from dual potential recordings. J Comput Neurosci. 11: 95-110 (2001). (DOI, PDF)

B.E. Griffith and C.S. Peskin. On the order of accuracy of the immersed boundary method: Higher order convergence rates for sufficiently smooth problems. J Comput Phys. 208: 75-105 (2005). (DOI, PDF)

B.E. Griffith, R.D. Hornung, D.M. McQueen, and C.S. Peskin. An adaptive, formally second order accurate version of the immersed boundary method. J Comput Phys. 223: 10-49 (2007). (DOI, PDF)

B.E. Griffith, X. Luo, D.M. McQueen, and C.S. Peskin. Simulating the fluid dynamics of natural and prosthetic heart valves using the immersed boundary method. Int J Appl Mech. 1: 137-177 (2009). (DOI, PDF)

P.E. Hand, B.E. Griffith, and C.S. Peskin. Deriving macroscopic myocardial conductivities by homogenization of microscopic models. Bull Math Biol. 71: 1707-1726 (2009). (DOI, PDF)

B.E. Griffith. An accurate and efficient method for the incompressible Navier-Stokes equations using the projection method as a preconditioner. J Comput Phys. 228: 7565-7595 (2009). (DOI, PDF)

P. Lee, B.E. Griffith, and C.S. Peskin. The immersed boundary method for advection-electrodiffusion with implicit timestepping and local mesh refinement. J Comput Phys. 229: 5208-5227 (2010). (DOI, PDF)

P.E. Hand and B.E. Griffith. Adaptive multiscale model for simulating cardiac conduction. Proc Natl Acad Sci U S A. 107: 14603-14608 (2010). (Paper: DOI, PDF; Supporting Information: HTTP, PDF)

P.E. Hand and B.E. Griffith. Empirical study of an adaptive multiscale model for simulating cardiac conduction. Bull Math Biol. 73: 3071-3089 (2011). (DOI, PDF)

B.E. Griffith. On the volume conservation of the immersed boundary method. Commun Comput Phys. 12: 401-432 (2012). (HTTP, PDF)

B.E. Griffith and S. Lim. Simulating an elastic ring with bend and twist by an adaptive generalized immersed boundary method. Commun Comput Phys. 12: 433-461 (2012). (HTTP, PDF)

B.E. Griffith. Immersed boundary model of aortic heart valve dynamics with physiological driving and loading conditions. Int J Numer Meth Biomed Eng. 28: 317-345 (2012). (DOI, PDF)

X.Y. Luo, B.E. Griffith, X.S. Ma, M. Yin, T.J. Wang, C.L. Liang, P.N. Watton, and G.M. Bernacca. Effect of bending rigidity in a dynamic model of a polyurethane prosthetic mitral valve. Biomechan Model Mechanobiol. To appear. (DOI)

H.M. Wang, H. Gao, X.Y. Luo, C. Berry, B.E. Griffith, R.W. Ogden, and T.J. Wang. Structure-based finite strain modelling of the human left ventricle in diastole. Int J Numer Meth Biomed Eng. To appear.

B.E. Griffith and X. Luo. Hybrid finite difference/finite element version of the immersed boundary. Submitted in revised form. (PDF)

F. Balboa, J.B. Bell, R. Delgado-Buscalioni, A. Donev, T. Fai, B.E. Griffith, and C.S. Peskin. Staggered schemes for fluctuating hydrodynamics. Submitted.

A.P.S. Bhalla, R. Bale, B.E. Griffith, and N.A. Patankar. A unified mathematical framework and an adaptive numerical method for fluid-structure interaction with rigid, deforming, and elastic bodies. Submitted.

Book Chapters

B.E. Griffith, R.D. Hornung, D.M. McQueen, and C.S. Peskin. Parallel and Adaptive Simulation of Cardiac Fluid Dynamics. In: Advanced Computational Infrastructures for Parallel and Distributed Adaptive Applications. M. Parashar and X. Li, eds. John Wiley and Sons. 2009. (PDF)

D.M. McQueen, T. O'Donnell, B.E. Griffith, and C.S. Peskin. Constructing a Patient-Specific Model Heart from CT Data. In: Handbook of Biomedical Imaging. N. Paragios, J. Duncan, and N. Ayache, eds. Springer-Verlag. To appear.

Conference Proceedings

B.E. Griffith, D.M. McQueen, and C.S. Peskin. Simulating cardiovascular fluid dynamics by the immersed boundary method. 47th AIAA Aerospace Sciences Meeting, 5-8 Jan 2009, Orlando, Florida. Paper Number AIAA-2009-158 (2009). (PDF)

Ph.D. Thesis

B.E. Griffith. Simulating the blood-muscle-valve mechanics of the heart by an adaptive and parallel version of the immersed boundary method. Ph.D. Thesis. Courant Institute of Mathematical Sciences, New York University (2005). (PS, PDF)